The report was being seen in Westminster as authoritative because Johnson recorded a broadcast interview with the BBC in which he was due to explain his thinking. He will formally outline his position in a Daily Telegraph column that is expected to be published at 10pm.

The move will come as a severe blow to David Cameron, who had pleaded with the London mayor earlier on Sunday to avoid “linking arms” with Nigel Farage and George Galloway in backing Britain’s exit from the EU. But by the weekend, the prime minister was pretty confident that Johnson would follow Michael Gove, the justice secretary and his close cabinet colleague, in campaigning to leave.

Opinion polls show that Johnson would have provided a significant boost to the campaign to stay had he decided to support the prime minister in the referendum.

A YouGov/Prospect survey last October found that the pro-EU majority would see its support increase from three points to 18 – a 15% bounce – if Johnson and Cameron both campaigned to remain. When voters were asked in a separate sample how they would vote if Cameron supported remain and Johnson supported leave, the bounce fell to eight points.

Johnson had been toying with various options over the last six months, but last week he indicated to close friends that he was leaning towards Brexit.

The mayor will have his work cut out to convince Tories at Westminster that he has made the decision, as Gove did, out of conviction and not because he believes that supporting a UK exit from the EU will boost his credentials as a future leader of the party.

In recent weeks Johnson had been overheard as saying that he was not an “outer”. He had also been flirting with Eurosceptic ideas that fell short of endorsing a UK exit from the EU, fuelling suspicions that he was calculating .

Sir Nicholas Soames, the former defence minister who is a Cameron loyalist, highlighted the Tory leadership’s suspicions about Johnson when he tweeted: “Whatever my great friend Boris decides to do I know that he is NOT an outer.”

Johnson spoke over the summer to Dominic Cummings, the Vote Leave campaign director and former Gove special adviser, to discuss his idea for two referendums.

When that idea was knocked down by the prime minister, Johnson alighted on the idea of finding a way to formally re-assert the sovereignty of the UK parliament.

Cameron said he would address this in an announcement next week, and was widely expected to introduce a bill to deal with the issue. The decision by Johnson to announce his intentions on Sunday was proof that he was unimpressed by the prime minister’s proposed offering.

Downing Street had seriously entertained the thought until last week that Johnson would eventually stand alongside the prime minister in supporting UK membership. Cameron believed Johnson had made a career, as a journalist and politician, grandstanding as a Eurosceptic while fundamentally believing that Britain should remain in the EU.

But the London mayor had made clear in recent months that he felt the prime minister had squandered an opportunity to table more ambitious demands. He urged Cameron to be “Dave the bold”.

The leave camp will be delirious that they have signed up one of the few politicians to attract adulation on the campaign trail. Johnson’s support will go a long way to ensuring that the leave camp avoids one of the main weaknesses of the no side in 1975 – that its leaders were seen as fringe politicians on the hard left and hard right.

Cameron is unlikely to forgive Johnson easily. He may well be minded to offer Johnson a lesser cabinet post should he win the referendum on 23 June. But Johnson will be in pole position to succeed Cameron as Tory if the prime minister loses the referendum.

Cameron said he would stay on to negotiate Britain’s exit from the EU if he loses the referendum. He said a similar thing before the Scottish independence referendum to ensure that his leadership did not become a distraction during the campaign. In private he wrote a resignation speech which he would have delivered if Scotland had voted to leave the EU.